Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
\[e^{\left(x + y \cdot \log y\right) - z}\]
↓
\[e^{\mathsf{fma}\left(y, \log y, x\right) - z}\]
e^{\left(x + y \cdot \log y\right) - z}
↓
e^{\mathsf{fma}\left(y, \log y, x\right) - z}
double f(double x, double y, double z) {
        double r129277 = x;
        double r129278 = y;
        double r129279 = log(r129278);
        double r129280 = r129278 * r129279;
        double r129281 = r129277 + r129280;
        double r129282 = z;
        double r129283 = r129281 - r129282;
        double r129284 = exp(r129283);
        return r129284;
}
↓
double f(double x, double y, double z) {
        double r129285 = y;
        double r129286 = log(r129285);
        double r129287 = x;
        double r129288 = fma(r129285, r129286, r129287);
        double r129289 = z;
        double r129290 = r129288 - r129289;
        double r129291 = exp(r129290);
        return r129291;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Target0.0
Herbie0.0
\[e^{\left(x - z\right) + \log y \cdot y}\]

Derivation

  1. Initial program 0.0

    \[e^{\left(x + y \cdot \log y\right) - z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{e^{\mathsf{fma}\left(y, \log y, x\right) - z}}\]

  3. Final simplification0.0

    \[\leadsto e^{\mathsf{fma}\left(y, \log y, x\right) - z}\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z)
  :name "Statistics.Distribution.Poisson.Internal:probability from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (exp (+ (- x z) (* (log y) y)))

  (exp (- (+ x (* y (log y))) z)))